Two-parameter bifurcations analysis of a delayed high-temperature superconducting maglev model with guidance force

Area of Science:

• Physics
• Engineering
• Applied Mathematics

Background:

• High-temperature superconducting (HTS) maglev systems are crucial for advanced transportation.
• Understanding the dynamic properties of HTS maglev models is essential for stability and control.
• Time delays can significantly alter system behavior, yet their impact on HTS maglev dynamics is not fully understood.

Purpose of the Study:

• To investigate the influence of time delay on the dynamic properties of a modified HTS maglev model.
• To analyze stability and bifurcations in both the time-delayed and undelayed systems.
• To explore complex dynamic phenomena such as chaos and multistability introduced by time delays.

Main Methods:

• Analysis of the original HTS maglev model without time delay using center manifold theorem and normal form theory.
• Investigation of co-dimension two bifurcations (Bautin and Hopf-Hopf) in the delayed HTS maglev model.
• Application of bifurcation theory for functional differential equations to calculate normal forms.
• Numerical simulations to explore system dynamics and generate bifurcation diagrams.

Main Results:

• The undelayed system exhibits periodic equilibrium points, with stability and Hopf bifurcations analyzed.
• The delayed system demonstrates co-dimension two bifurcations, including Bautin and Hopf-Hopf bifurcations.
• Numerical simulations reveal abundant dynamic phenomena, such as periodic coexistence and multistability.
• Introduction of time delay leads to chaotic behavior and more complex displacement-velocity relationships.

Conclusions:

• Time delay is a critical factor influencing the dynamic behavior of HTS maglev systems.
• The delayed HTS maglev model exhibits richer and more complex dynamics than the undelayed model.
• Findings provide deeper insights into the stability and control of HTS maglev systems under time-delayed conditions.